When teachers end up physically fighting among themselves often, yes principal is responsible. Absolutely. Principal should have deal with the problem when it appeared first time. Principal is responsible for school culture.
Holding the CEO liable for employee misdeeds is like holding a principal responsible for students getting into fights or having sex.
Just like the principal doesn’t choose the students, management often only hires their direct subordinates. The principal/CEO could expel students/employees directly, but it’s often met with opposition, more the further down the hierarchy they reach.
But, teachers are allowed to have sex.